At about 3 km/s, an object's kinetic energy is the same as the chemical energy an equal mass of chemical explosives would have. Thus above that point there's little increase in damage to be had from explosive warheads (just put any spare mass into fuel to get a higher terminal velocity).
One G for 1,000 seconds get you 10 km/s, for about ten times the energy of this threshold
Nukes are enormously more powerful, especially in terms of bang per kilogram. One that'll fit onto a standard CT missile will be quite weak, say 1 kiloton, because most of its mass will be non-nuclear control systems, chemical initiators, and so on. But even 1 kT for a 0.1 ton missile means the missile needs to be going about 300 km/s to have the same energy density from kinetic energy (five 1,000s turns at 6G), and a nuke brings a stand-off capability as well - no need to get an actual contact hit.
So nukes are very definitely worth it as long as dampers aren't all-powerful. They make hits easier and bring a huge increase in damage potential.